Coherent light scattering and resonant energy transfer in an apertureless scanning near-field optical microscope Jaromı ´ r Fiura ´ s ˇ ek, Boris Chernobrod, Yehiam Prior, and Ilya Sh. Averbukh * Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel Received 18 June 2000; revised manuscript received 23 October 2000; published 9 January 2001 We investigate the interaction of two molecules or nanosized particles with a nearly resonant laser field under the tip of an apertureless near-field microscope. We show that interference of several scattering channels provides means for enhanced spatial resolution. The visibility of two separate nano objects is considered, and a natural definition emerges for the resolution of the apertureless microscope operating under conditions of nearly resonant illumination. The probe tip creates an additional coupling channel between the two molecules, and thus affects the energy transfer between them. We demonstrate that the tip can either enhance or suppress this transfer. Two models for the tip geometry are considered: a simplified pointlike dipole, and a more realistic elongated spheroid. Quantitative results are obtained for the dependence on irradiation frequency and tip position for dielectric as well as metallic tips. In particular, specific results are obtained for a silver tip under conditions of plasmon resonance, and we show that under fully resonant conditions the tip may enhance the intermolecular energy transfer by nearly two orders of magnitude. DOI: 10.1103/PhysRevB.63.045420 PACS numbers: 87.64.Xx, 41.20.Cv I. INTRODUCTION Recent progress in the spectroscopy of single molecules is closely related to advances in microscopy at suboptical wavelength resolution obtained via scanning near-field opti- cal microscopy SNOM. 1–8 Many variants of near-field op- tical microscopes employ single-mode optical fibers tapered at their end and possibly metal coated to form a subwave- length aperture. The typical resolution of these systems is of the order of tens of nanometers, limited by the penetration of evanescent fields through the metal coating of the fiber. Moreover, aperture-based scanning near-field optical micro- scopes often suffer from limitations on the optical power which can be delivered through the subwavelength aperture. Both of these problems are alleviated by apertureless schemes, 9–19 in which a sharp nanosized probe near the sur- face is illuminated from the outside by an external light source. This approach is based on an enhancement of optical fields in close proximity to a sharp tip. The enhancement effect has a twofold origin: First, the field increases due to a pure geometrical reason, the so-called ‘‘lightening rod’’ effect, 20–22 and further enhancement arises due to excitation of localized plasmons in a metallized tip. 13,20,23 Localized strong fields near the sharp tip enable various nanoscopic applications. The field enhancement locally in- creases the efficiency of nonlinear optical processes such as two-photon absorption 24,25 or local second-harmonic genera- tion from a rough metallic surface. 26 Resonantly excited sur- face plasmons propagating along a silver/air interface can be locally probed by an apertureless SNOM tip. 27 A small di- electric particle, lying in a vicinity of the sharp tip, is sub- jected to strong forces arising from large near-field gradient, so that the tip can serve as nanometric optical tweezers, al- lowing for trapping and alignment of dielectric nanoparticles. 28 In scanning experiments, near-field interactions between the probe and the sample can dramatically enhance light scattering from the observed object, because the tip acts as an efficient ‘‘antenna,’’ and the tip-object system scatters light in a cooperative manner. As a result, such a system has the potential of achieving single-molecule sensitivity, espe- cially when exciting resonant molecular transitions. 14,29,30 Localization of the enhanced near field in the vicinity of the tip enables one to examine local properties of the sample. As we recently showed, coherent tip-sample interactions manifest themselves in the dependence of the total scattered intensity on the amplitudes and phases of the complex polar- izabilities of the sample and the tip. 30 As a result, sub- nanometer localization of a single object e.g., a molecule is possible when the scattered intensity is detected. However, one has to distinguish between localization and resolution, and in order to define the resolution of such experiments, the detection of at least two nearby objects must be considered. In this paper, we examine the detection of two closely lying molecules or other small objects by an apertureless SNOM device. Molecules are described as pointlike dipoles with well defined resonant frequencies, polarizabilities, and decay rates. In particular, we concentrate on the case of light which is nearly resonant with the molecular transitions, and the tip plasmon resonances are also not too far detuned. When the distance between the molecules is small enough, they can exchange energy via resonant dipole-dipole interac- tion even in the absence of the tip. An approaching tip, how- ever, significantly modifies the molecular attributes resonant frequencies and decay rates, 31–36 and we show that, in ad- dition, the tip creates another coupling channel between the molecules. As a result, a properly positioned tip can be used to control the energy transfer, or more generally the cou- pling, between the molecules. A discussion of the energy exchange between two atoms, one inside a dielectric micro- sphere and the other placed near its outer surface, was re- cently presented. 36 Theoretical descriptions of the tip-sample interaction in an apertureless SNOM device were based on numerical so- lutions of Maxwell equations, and several numerical PHYSICAL REVIEW B, VOLUME 63, 045420 0163-1829/2001/634/04542010/$15.00 ©2001 The American Physical Society 63 045420-1